Optimizing the search for transiting planets in long time series

Context: Transit surveys, both ground- and space- based, have already accumulated a large number of light curves that span several years. Aims: The search for transiting planets in these long time series is computationally intensive. We wish to optimize the search for both detection and computational efficiencies. Methods: We assume that the searched systems can be well described by Keplerian orbits. We then propagate the effects of different system parameters to the detection parameters. Results: We show that the frequency information content of the light curve is primarily determined by the duty cycle of the transit signal, and thus the optimal frequency sampling is found to be cubic and not linear. Further optimization is achieved by considering duty-cycle dependent binning of the phased light curve. By using the (standard) BLS one is either rather insensitive to long-period planets, or less sensitive to short-period planets and computationally slower by a significant factor of ~330 (for a 3yr long dataset). We also show how the physical system parameters, such as the host star's size and mass, directly affect transit detection. This understanding can then be used to optimize the search for every star individually. Conclusions: By considering Keplerian dynamics explicitly rather than implicitly one can optimally search the BLS parameter space. The presented Optimal BLS enhances the detectability of both very short and very long period planets while allowing such searches to be done with much reduced resources and time. The Matlab/Octave source code for Optimal BLS is made available.Comment: 7 pages, 4 figures, 1 table. A&A accepted. Source code is available at: http://www.astro.physik.uni-goettingen.de/~avivofir

Position angles and coplanarity of multiple systems from transit timing

Aims: We compare the apparent difference in timing of transiting planets (or eclipsing binaries) that are observed from widely separated locations (parallactic delay). Methods: A simple geometrical argument allow us to show that the apparent timing difference depends also on the on-sky position angle of the planetary (or secondary) orbit, relative to the ecliptic plane. Results: We calculate that on-sky position angle would be readily observable using the future PLATO and CHEOPS missions data, and possibility observable already in many known radial-velocity systems (if they exhibit transits). We also find that on-sky coplanarity of multiple objects in the same system can be probed more easily than the on-sky position angle of each of the objects separately. We calculate the magnitude of the effect for all currently known planets (should they exhibit transits), finding that almost 200 of them -- mostly radial-velocity detected planets -- have predicted timing effect larger than 1 second. We also compute the theoretical timing precision for the PLATO mission, that will observe a similar stellar population, and find that a 1 second effect would be frequently readily observable. We also find that on-sky coplanarity of multiple objects in the same system can be probed more easily than the on-sky position angle of each of the objects separately. Conclusions: We show a new observable from transit photometry becomes available when very high precision transit timing is available. We find that there is a good match between projected capabilities of the future space missions PLATO and CHEOPS and the new observable. We give some initial science question that such a new observable may be related to and help addressing.Comment: 4 pages, 2 figures. A&A accepte

Identifying Transiting Circumbinary Planets

Transiting planets manifest themselves by a periodic dimming of their host star by a fixed amount. On the other hand, light curves of transiting circumbinary (CB) planets are expected to be neither periodic nor to have a single depth while in transit, making BLS [Kovacs et al. 2002] almost ineffective. Therefore, a modified version for the identification of CB planets was developed - CB-BLS. We show that using CB-BLS it is possible to find CB planets in the residuals of light curves of eclipsing binaries (EBs) that have noise levels of 1% or more. Using CB-BLS will allow to easily harness the massive ground- and space- based photometric surveys to look for these objects. Detecting transiting CB planets is expected to have a wide range of implications, for e.g.: The frequency of CB planets depend on the planetary formation mechanism - and planets in close pairs of stars provides a most restrictive constraint on planet formation models. Furthermore, understanding very high precision light curves is limited by stellar parameters - and since for EBs the stellar parameters are much better determined, the resultant planetary structure models will have significantly smaller error bars, maybe even small enough to challenge theory.Comment: To appear on the IAU Symposium 253 proceedings. 4 pages, 4 figure

The Advantages of Global Photometric Models in Fitting Transit Variations

Estimation of planetary orbital and physical parameters from light-curve data relies heavily on the accurate interpretation of Transit Timing Variations (TTV) measurements. In this letter, we review the process of TTV measurement and compare two fitting paradigms - one that relies on making transit-by-transit timing estimates and then fitting a TTV model to the observed timings and one that relies on fitting a global flux model to the entire light-curve data simultaneously. The latter method is achieved either by solving for the underlying planetary motion (often referred to as "photodynamics"), or by using an approximate or empirical shape of the TTV signal. We show that across a large range of the transit SNR regime, the probability distribution function (PDF) of the mid-transit time significantly deviates from a Gaussian, even if the flux errors do distribute normally. Treating the timing uncertainties as if they are distributed normally leads, in such a case, to a wrong interpretation of the TTV measurements. We illustrate these points using numerical experiments and conclude that a fitting process that relies on a global flux fitting rather than the derived TTVs, should be preferred.Comment: 12 pages, 5 figure